Method and arrangement for coding transform coefficients in picture and/or video coders and decoders and a corresponding computer program and a corresponding computer-readable storage medium

ABSTRACT

The present invention describes a method and an arrangement for coding transform coefficients in picture and/or video coders and decoders and a corresponding computer program and a corresponding computer-readable storage medium, which can particularly be employed as a novel efficient method for binary-arithmetic coding transform coefficients in the field of video coding. 
     For this, it is suggested that, for blocks of (video) pictures containing significant transform coefficients, coding of the transform coefficients takes place in such a way that, for each block in a scan process, the positions of significant transform coefficients in the block and subsequently, in a reverse scan order—starting from the last significant transform coefficient within the block—the values (levels) of the significant transform coefficients are determined and coded.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of co-pending U.S. patent application Ser. No. 12/428,139 filed on Apr. 22, 2009, which will issue as U.S. Pat. No. 9,362,949 on Jun. 7, 2016, which is a continuation of U.S. patent application Ser. No. 10/727,802, filed on Dec. 4, 2003, now U.S. Pat. No. 7,702,013, which is a continuation of International Application No. PCT/EP03/04656, filed May 2, 2003, which designated the United States and was not published in English; the application also claims the priority under 35 U.S.C. §119, of German patent application No. DE 102 20 961.8, filed May 2, 2002; those applications being incorporated herein, by reference, in their entireties.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention describes a method and an arrangement for coding transform coefficients in picture and/or video coders and decoders and a corresponding computer program and a corresponding computer-readable storage medium, which can particularly be employed as a novel efficient method for binary-arithmetic coding transform coefficients in the field of video coding (CABAC in H.264/AVC cf. [1]).

Description of the Related Art

In present hybrid block-based standards for video coding, such as, for example, MPEG-2 [2], H.263 [3] and MPEG-4 [4], the blocks of quantized transform coefficients (levels) are mapped by a defined scan process to a vector which is coded to code words having a variable length by using a run-length coding and subsequent mapping.

In MPEG-2 [2], the code words having a variable length are associated to two-dimensional events (RUN, LEVEL), wherein LEVEL represents the quantized value of a (significant) transform coefficient not quantized to zero; the run-length RUN indicates the number of subsequent (non-significant) transform coefficients quantized to zero, which, in the vector of transform coefficients, are immediately in front of the present significant transform coefficients. In addition, code words having a variable length are defined for the two special events EOB and ESCAPE. While the EOB event indicates that there are no further significant transform coefficients in the block, the ESCAPE event signals that the existing event (RUN, LEVEL) cannot be represented by the defined alphabet of code words having a variable length. In this case, the symbols RUN and LEVEL are coded by code words of a fixed length.

In the newer coding standards H.263 [3] and MPEG-4 [4], the association of code words having a variable length takes place on the basis of three-dimensional events (LAST, RUN, LEVEL), wherein the binary symbol LAST indicates whether the present significant transform coefficient is the last significant coefficient within the block or whether further significant transform coefficients follow. By using these three-dimensional events, no additional EOB event is required; an ESCAPE event is used in analogy to MPEG-2, wherein the binary symbol LAST is coded additionally to RUN and LEVEL.

The coding of the transform coefficients realized in MPEG-2, H.263 and MPEG-4 has the following disadvantages:

-   -   To each coding event only a code word having an integer length         can be associated, an efficient coding of events with         probabilities larger than 0.5 cannot take place.     -   The usage of a fixed table for mapping the coding events to the         code word having a variable length for all the transform         coefficients within a block does not consider symbol statistics         depending on position or frequency.     -   Adaptation to the actually existing symbol statistics is not         possible.     -   No usage is made of inter-symbol redundancies present.

Annex E of the H.263 standard specifies an optional non-adaptive arithmetic coding in which different predetermined model probability distributions are used,

-   -   one each for the first, second and third event (LAST, RUN,         LEVEL)/ESCAPE     -   another one for all the following events (LAST, RUN,         LEVEL)/ESCAPE of a block of transform coefficients,     -   as well as one each for the symbols LAST, RUN and LEVEL, which         are coded after an ESCAPE event.

For the following reasons no appreciable increase of the coding efficiency is, however, possible by this optional arithmetic coding:

-   -   The advantage of arithmetic coding that a code word having a         non-integer length can be associated to a coding event hardly         has any effect on the coding efficiency by using combined events         of the form (LAST, RUN, LEVEL).     -   The advantage of using different probability distributions is         eliminated by the fact that adaptation to the actually present         symbol statistics is not possible.

One of the first published methods for coding transform coefficients by an adaptive binary arithmetic coding in a hybrid video coder ensuring the adaptation of probabilities to the symbol statistics present has been presented in [5].

In H.264/AVC [1], a context-adaptive method on the basis of code words having a variable length for coding transform coefficients is specified as the standard method for entropy coding. Here, the coding of a block of transform coefficients is determined by the following characteristics:

-   -   Both the number of the significant coefficients within a block         and the number of subsequent coefficients quantized to one at         the end of the vector of transform coefficients are determined         by a symbol COEFF_TOKEN. Depending on the block type and the         symbols COEFF_TOKEN already coded/decoded for neighboring         blocks, one of five defined code word tables is chosen for         coding.     -   While for the transform coefficients quantized to one at the end         of the coefficient vector only a single bit is transferred for         specifying the sign, the coding of the values (levels) of the         remaining significant transform coefficients takes place in a         reverse scan order by means of a combined prefix suffix code         word.     -   If the number of significant transform coefficients is smaller         than the number of transform coefficients for the corresponding         block, a symbol TOTAL_ZEROS will be coded, which indicates the         number of transform coefficients quantized to zero which, in the         coefficient vector, are in front of the last significant         coefficient. For this, 18 code word tables have been specified,         which are switched depending on the number of significant         coefficients and the block type.     -   The run-length of the (non-significant) coefficients quantized         to zero (RUN) in front of a significant coefficient is coded for         each significant transform coefficient in a reverse scan order         as long as the sum of RUNs already coded is smaller than         TOTAL_ZEROS. Depending on TOTAL_ZEROS and the RUNs already         coded/decoded, switching between seven code word tables takes         place.

Although this so-called CAVLC method (CAVLC: context-adaptive variable length coding), by context based switching the code word tables, allows a considerably more efficient coding of the transform coefficients than the methods specified in MPEG-2, H.263 and MPEG-4, it basically has the following disadvantages:

-   -   Switching between different code word tables takes place         depending on symbols already coded/decoded, the code word         tables, however, cannot be adjusted to the actual symbol         statistics.     -   By using code words having a variable length, events having         symbol probabilities larger than 0.5 cannot be coded         efficiently. This limitation especially prevents coding symbols         having a smaller value range, by means of which a construction         of suitable contexts might be possible for switching between         different model probability distributions.

A possible solution for avoiding the disadvantages illustrated of well-known methods for coding transform coefficients in block-based picture and video coders is a combination of an adaptive arithmetic coding and a suitable context generation for using the inter-symbol redundancies. Since the more complicated computing of the arithmetic coding, compared to coding by means of code words having a variable length, is a disadvantage, the possibility of an efficient hardware and software implementation must be considered particularly.

SUMMARY OF THE INVENTION

Thus, it is the object of the present invention to provide a method and an arrangement for coding transform coefficients in picture and/or video coders and decoders and a corresponding computer program and a corresponding computer-readable storage medium, which eliminate the deficiencies mentioned above and, in particular, keep the amount of calculating required for coding small.

In accordance with a first aspect, the present invention provides a method for coding transform coefficients in picture and/or video coders and decoders, wherein for blocks of (video) pictures containing significant transform coefficients, the coding of transform coefficients takes place in such a way that, for each block,

-   -   in a scan process, the positions of significant transform         coefficients in the block and subsequently,     -   in a reverse scan order—starting with the last significant         transform coefficients within the block—the values (levels) of         the significant transform coefficients         are determined and coded.

One preferred embodiment of the inventive method is characterized by each significant transform coefficient of the block other than the last transform coefficient of the block being characterized by a one-bit symbol.

It is also of advantage if the sign for each significant transform coefficient is indicated by a one-bit symbol (SIGN) and the magnitude is indicated by a binary coded symbol (ABS).

In one preferred embodiment of the inventive method, blocks containing significant transform coefficients are characterized by a one-bit symbol CBP4 in connection with other syntax elements, such as, for example, CBP or macro block mode.

It is a special advantage of the method that, by transferring a one-bit symbol SIG for each coefficient of a block and of a one-bit symbol LAST for each significant coefficient of a block, a significance mapping is coded, wherein the transfer takes place in the scan order, SIG serves for identifying significant coefficients and LAST indicates whether there are further significant transform coefficients in the block.

In another preferred embodiment of the inventive method, modeling for the one-bit symbol CBP4, for coding the significance mapping and/or for coding the coefficient magnitudes takes place in a context-dependent way. Thus, block types of transform coefficients having comparable statistics are summarized to block categories.

It is also of advantage that, in a special embodiment of the inventive method, no significance information (SIG, LAST) is transferred for the last scan position of a block.

In a preferred embodiment of the inventive method, the magnitude (ABS) is indicated by a symbol in unary binarization or by a symbol having a prefix part and a suffix part, wherein the prefix part consists of ones and the suffix part is coded in a 0th order exp-golomb code.

In accordance with a second aspect, the present invention provides an arrangement having at least one processor and/or chip formed such that method for coding transform coefficients in picture and/or video coders and decoders can be performed, wherein for blocks of (video) pictures containing significant transform coefficients, the coding of transform coefficients takes place in such a way that, for each block,

-   -   in a scan process, the positions of significant transform         coefficients in the block and subsequently,     -   in a reverse scan order—starting with the last significant         transform coefficients within the block—the values (levels) of         the significant transform coefficients         are determined and coded.

In accordance with a third aspect, the present invention provides a computer program enabling a computer, after having been loaded into the memory of the computer, to perform a method for coding transform coefficients in picture and/or video coders and decoders, wherein for blocks of (video) pictures containing significant transform coefficients, the coding of transform coefficients takes place in such a way that, for each block,

-   -   in a scan process, the positions of significant transform         coefficients in the block and subsequently,     -   in a reverse scan order—starting with the last significant         transform coefficients within the block—the values (levels) of         the significant transform coefficients         are determined and coded.

Such computer programs can, for example, (for a fee or free of charge, freely accessible or protected by a password) be provided in a data or communication network for downloading. The computer programs provided in this way can then be utilized by a method in which a computer program according to claim 11 is downloaded from a network for transfer, such as, for example, from the Internet, to data processing means connected to the network.

In accordance with a fourth aspect, the present invention provides a computer-readable storage medium on which a program is stored, enabling a computer, after having been loaded into the memory of the computer, to perform a method for coding transform coefficients in picture and/or video coders and decoders, wherein for blocks of (video) pictures containing significant transform coefficients, the coding of transform coefficients takes place in such a way that, for each block,

-   -   in a scan process, the positions of significant transform         coefficients in the block and subsequently,     -   in a reverse scan order—starting with the last significant         transform coefficients within the block—the values (levels) of         the significant transform coefficients         are determined and coded.

The novel method for coding transform coefficients is especially characterized by the following characteristics:

-   -   A two-dimensional block of transform coefficients is mapped to a         one-dimensional vector by a scan process.     -   The syntax elements of the EOB symbol, the LAST symbol or the         coefficient counter (number of significant coefficients) as well         as RUN (number of non-significant coefficients in the scan         order) used in well-known methods are replaced by a one-bit         symbol CBP4 and a significance mapping.     -   The levels (magnitudes of the significant coefficients) are         coded in a reverse scan order.     -   Context modeling takes place in a novel manner.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

Preferred embodiments of the present invention will be detailed subsequently referring to the appended drawings, in which:

FIG. 1 is an illustration of the basic principle of coding transform coefficients according to the inventive coding method,

FIG. 2 shows two examples for coding the significance mapping (the yellow marked symbols are not transferred),

FIG. 3 shows binarization for the magnitudes of the transform coefficients (ABS),

FIG. 4 shows block types and their classification for the H.264/AVC standard,

FIG. 5 shows context modeling for the one-bit symbol CBP4, and

FIG. 6 shows examples of the context modeling for coding the magnitudes of the significant transform coefficients.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 illustrates the novel coding method. For each block of transform coefficients, a one-bit symbol CBP4 is transferred at first, unless higher order syntax elements (CBP or macro block mode) already indicate that the block considered does not contain any significant transform coefficients. The CBP4 symbol will be zero if there are no significant coefficients in the block. If it is one, a significance mapping specifying the position (in scan order) of the significant transform coefficients will be coded. Subsequently, the magnitude and the signs of the significant coefficients are transferred in a reverse scan order. A detailed description of the coding process will be given below in 1. Afterwards, context modeling for the binary arithmetic coding will be described in 2.

1. Description of the Coding of the Transform Coefficients

1.1 Scanning Transform Coefficients

The transform coefficients of each block are mapped to a vector by means of a scan process (such as, for example, a zig zag scan).

1.2 CBP4 Symbol

CBP4 is a one-bit symbol indicating whether there are significant transform coefficients (transform coefficients unequal to zero) in a block. If the CBP4 symbol is zero, no further information for the corresponding block will be transferred.

1.3 Significance Mapping

If the CBP4 symbol indicates that the corresponding block contains significant coefficients, a significance mapping will be coded. This takes place by transferring a one-bit symbol (SIG) for each coefficient in the scan order. If a corresponding significance symbol is one (significant coefficient), another one-bit symbol (LAST) will be transferred. This symbol indicates whether the present significant coefficient is the last significant coefficient within a block or whether further significant coefficients follow. FIG. 2 shows two examples of the method described for coding the significance mapping. Significance information (SIG, LAST) will never be transferred for the last scan position of a block. If the transfer of the significance mapping has not already been terminated by a LAST symbol of one, it is obvious that the coefficient at the last scan position is significant (see yellow marked position in FIG. 2).

1.4 Level Information

The positions of the significant transform coefficients within a block are clearly specified by the significance mapping. The coding of the precise values of the coefficients (levels) takes place by two coding symbols: ABS (magnitude of the coefficients) and SIGN (sign of the coefficients). While SIGN represents a one-bit symbol, binarization according to FIG. 3 is used for coding the magnitudes of the coefficients (ABS). For coefficient magnitudes in the interval [1; 14], this binarization corresponds to a unary binarization. The binarization for coefficient magnitudes larger than 14 consists of a prefix part consisting of 14 ones and a suffix part representing a 0th order exp-golomb code for the symbol (ABS-15). Binarization does not include a representation for coefficient magnitudes (ABS) equaling 0, since significant coefficients (coefficients unequal to zero) will always have a magnitude (ABS) larger than or equal to one.

The binarization formed of a prefix part and a suffix part consisting of a 0th order exp-golomb code for coefficient magnitudes larger than 14 has the advantage that a special non-adaptive context with symbol probabilities 0.5 can be used without sacrificing in coding efficiency for all the binary decisions of the suffix part, whereby the amount of calculating for encoding and decoding can be reduced.

The levels are coded in a reverse scan order—beginning with the last significant coefficient within the block; this enables forming suitable contacts for the binary arithmetic coding.

2. Context Modeling

In general, different types of transform coefficient blocks are differentiated when considering a picture and/or video coding system. Thus, there are, for example, twelve types of transform coefficient blocks, having different statistics (the left column of table in FIG. 4) in the present Final Draft International Standard [1] of the H.264/AVC standard. For most picture sequences and coding conditions, some of the statistics are, however, very similar. In order to keep the number of contexts used small and thus to ensure a quick adaptation to the statistic of the picture sequence to be coded, the block types, in the H.264/AVC standard, can, for example, be classified into five categories (see right column of table in FIG. 4). Similar classifications are possible for other picture and/or video coding systems. For each of the—in the case of the H.264/AVC standard—five categories, an individual quantity of contexts is used for the symbols CBP4, SIG, LAST and ABS.

2.1 Context Modeling for the CBP4 Symbol

For coding the one-bit symbol CBP4, four different contexts are used for each individual category of transform blocks (see FIG. 5). The context number for block C to be coded is determined by

-   -   i) ctx_number_cbp4 (C)=CBP4 (A)+2×CBP4 (B)

wherein those neighboring blocks (left and top) of block C considered to be associated to the same block type are designated by A and B. Regarding the H.264/AVC standard, the following 6 block types are differentiated for this conditioning: Luma-DC, Luma-AC, Chroma-U-DC, Chroma-U-AC, Chroma-V-DC and Chroma-V-AC. If the concerning block X (A or B) of transform coefficients does not exist in a neighboring macro block (this is, for example, the case if the present block is coded in the INTRA16×16 mode, but the neighboring block has been transferred in an INTER mode), CBP4 (X) is set to zero for the neighboring block X. If a neighboring block X (A or B) is outside the picture area or belongs to another slice, the corresponding value CBP4 (X) is replaced by a default value. A default value of one is used for INTRA-coded blocks and a default value of zero is used for INTER-coded blocks.

2.2 Context Modeling for Coding the Significance Mapping

For coding the significance mapping, max_koeff−1 different contexts are each used per block category (see FIG. 4) for coding the symbols SIG and LAST. max_koeff thus designates the number of transform coefficients for the corresponding block category (for H.264/AVC, see FIG. 4). The context number is always indicated by the corresponding scan position of the coefficient considered. The context numbers of a coefficient koeff[i], which has been scanned as an i-th coefficient, thus result in:

-   -   i) ctx_number_sig(koeff[i])=ctx_number_last(koeff[i])=i.

2*max_koeff−2 contexts are used for each category of block types for coding the significance mapping.

2.3 Context Modeling for Coding Coefficient Magnitudes

The binarization illustrated in FIG. 3 is used for coding the magnitudes of the significant transform coefficients. Two different context quantities are used per block category, namely one for coding the first binary decision bin=1 (FIG. 3) and another one for coding the binary decisions bin=2 . . . 14 (FIG. 3) of the binarization. The context numbers are thus associated as follows:

ctx_number_abs_1bin

-   -   i)=(koeff with ABS>1 coded ? 4:         -   (1) max(3, number of coded coefficients with ABS=1)),

ctx_number_abs_rbins

-   -   i)=max(4, number of coded coefficients with ABS>1)).

The magnitudes of the transform coefficients are transferred in a reverse scan order. The context for the first binary decision is determined by the number of coefficients already transferred (in reverse scan order) having a magnitude of ABS=1. If more than three coefficients with a magnitude ABS=1 have already been transferred, context number 3 will always be chosen. As soon as a coefficient having a magnitude ABS>1 has been transferred, context 4 will be used for all the remaining significant coefficients within the block.

All binary decisions with bin=2 . . . 14 are coded using one and the same context. Thus, the context number is determined by the number of coefficients already coded (in a reverse scan order) having a magnitude of ABS>1, wherein the maximum context number is limited to 4. For illustration, two examples for the context selection, when coding the magnitudes ABS of the significant transform coefficients, are illustrated in FIG. 6. For coding the binary decision bin>14 for the coefficient magnitudes and for the signs SIGN, an individual non-adaptive context with the symbol probabilities P₀=P₁=0.5 is used.

The invention, in its embodiment, is not limited to the preferred embodiments indicated hereinbefore. A number of variations making use of the inventive arrangement and of the inventive method, even if the design is completely different, are feasible.

While this invention has been described in terms of several preferred embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, and equivalents as fall within the true spirit and scope of the present invention.

REFERENCE LIST

-   [1] T. Wiegand, G. Sullivan, “Draft Text of Final Draft     International Standard (FDIS) of Joint Video Specification (ITU-T     Rec. H.264 | ISO/IEC 14496-10 AVC)”, JVT-G050, March 2003. -   [2] ITU-T and ISO/IEC JTC1, “Generic coding of moving pictures and     associated audio information—Part 2: Video”, ITU-T Recommendation     H.262—ISO/IEC 13818-2 (MPEG-2), November 1994 -   [3] ITU-T, “Video coding for low bitrate communications”, ITU-T     Recommendation H.263; version 1, November 1995, version 2, January     1998. -   [4] ISO/IEC JTC1, “Coding of audio-visual objects—Part 2: Visual”,     ISO/IEC 14496-2 (MPEG-4 visual version 1), April 1999; Amendment 1     (version 2), February 2000; Amendment 4 (streaming profile), January     2001. -   [5] C. A. Gonzales, “DCT coding of motion sequences including     arithmetic coder”, ISO-IEC/JTC1/SC2/WG8, MPEG 89/187, August 1989. 

The invention claimed is:
 1. A method for video decoding, the method being performed on a microprocessor or a computer, and comprising the steps of: decoding a coding of a significance mapping; and decoding a subsequent coding of values of transform coefficients being unequal to zero for blocks of video pictures containing transform coefficients being unequal to zero, wherein the significance mapping specifies the positions of the transform coefficients being unequal to zero in a scan order and comprises, in the scan order, —except for the last scan position in the scan order—a one-bit symbol (SIG) for each coefficient of the block and a one-bit symbol (LAST) for each significant coefficient of the block, wherein (SIG) serves for identifying significant coefficients and (LAST) indicates whether there are further significant transform coefficients in the block, and the coding of values of transform coefficients being unequal to zero comprises coded values of the transform coefficients being unequal to zero in a reverse scan order—starting from the last transform coefficient being unequal to zero, wherein the decoding a coding of the significance mapping comprises arithmetically decoding the significance mapping; and wherein the decoding the subsequent coding of the values of the transform coefficients comprises arithmetically decoding the coded values of transform coefficients being unequal to zero in reverse scan order, wherein magnitudes of the transform coefficients being unequal to zero are binarized into a binarization and at least one binary decision of the binarization is decoded by context-adaptive binary arithmetic decoding.
 2. The method according to claim 1, wherein each significant transform coefficient of the block other than the last transform coefficient of the block is characterized by a one-bit symbol.
 3. The method according to claim 1, wherein for each significant transform coefficient, the sign is indicated by a one-bit symbol (SIGN) and the magnitude is indicated by a binary-coded symbol (ABS).
 4. The method according to claim 1, wherein the arithmetically decoding of the values of the transform coefficients comprises indicating the magnitude by a symbol (ABS) having a prefix part and a suffix part, wherein the prefix part consists of ones and the suffix part is coded in a 0th order exp-golomb code.
 5. The method according to claim 1, wherein blocks containing significant transform coefficients are recognized on the basis of a one-bit symbol CBP4 in connection with further syntax elements.
 6. The method according to claim 5, wherein modeling for the one-bit symbol CBP4, or for coding the significance mapping and/or takes place in a context-dependent way.
 7. A device for decoding a coding of a significance mapping and a subsequent coding of values of transform coefficients being unequal to zero for blocks of video pictures containing transform coefficients being unequal to zero, wherein the significance mapping specifies the positions of the transform coefficients being unequal to zero in a scan order and comprises, in the scan order, —except for the last scan position in the scan order—a one-bit symbol (SIG) for each coefficient of the block and a one-bit symbol (LAST) for each significant coefficient of the block, wherein (SIG) serves for identifying significant coefficients and (LAST) indicates whether there are further significant transform coefficients in the block, and the coding of values of transform coefficients being unequal to zero comprise coded values of the transform coefficients being unequal to zero in a reverse scan order—starting from the last transform coefficient being unequal to zero, wherein the device comprises an arithmetic decoder for decoding the significance mapping; and the arithmetic decoder for decoding the coded values of transform coefficients being unequal to zero in reverse scan order, wherein magnitudes of the transform coefficients being unequal to zero are binarized into a binarization and at least one binary decision of the binarization is decoded by context-adaptive binary arithmetic decoding.
 8. A non-transitory computer-readable storage medium on which a program is stored, enabling a computer, after having been loaded into the memory of the computer, to perform a method for video coding, the method comprising: for each block of pictures of a video which contains significant transform coefficients, coding a significance mapping specifying the positions of significant transform coefficients in the respective block in a scan order, the coding of the significance map including: coding, in the scan order, —except for the last scan position in the scan order—a one-bit symbol (SIG) for each coefficient of the respective block and a one-bit symbol (LAST) for each significant coefficient of the respective block, wherein (SIG) serves for identifying significant coefficients and (LAST) indicates whether there are further significant transform coefficients in the respective block, and subsequently, in a reverse scan order—starting with the last significant transform coefficients within the block-arithmetically coding the values (levels) of the significant transform coefficients, wherein magnitudes of the transform coefficients being unequal to zero are binarized into a binarization and at least one binary decision of the binarization is decoded by context-adaptive binary arithmetic decoding. 